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Math Help - Common factor help

  1. #1
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    Common factor help

    Need some help on a easy question that i can't remenber how to do it
    \frac{1}{7^{3^{n+1}}} + \frac{1}{7^{3^{n+2}}} + ...
    \frac{1}{7^{3^{n+1}}} (1+ \frac{1}{7^{x}} + ...)

    What should x be?

    Thank you
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  2. #2
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    Quote Originally Posted by kleenex View Post
    Need some help on a easy question that i can't remenber how to do it
    \frac{1}{7^{3^{n+1}}} + \frac{1}{7^{3^{n+2}}} + ...
    \frac{1}{7^{3^{n+1}}} (1+ \frac{1}{7^{x}} + ...)

    What should x be?

    Thank you
    We need to satisfy \frac{1}{7^{3^{n+1}}}\cdot \frac{1}{7^x} = \frac{1}{7^{3^{n+2}}}.
    Thus, 7^{3^{n+1}}\cdot 7^x = 7^{3^{n+2}}
    Thus, 3^{n+1} + x = 3^{n+2}.
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